Redemption price per share or per unit of warrants or rights outstanding.

No definition available.

Name:	fiac_ClassOfWarrantOrRightRedemptionPriceOfWarrantsOrRights
Namespace Prefix:	fiac_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Period to provide written notice to redeem warrants, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_NoticePeriodToRedeemWarrants
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Number of trading days for common stock price to exceed threshold, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_NumberOfTradingDays
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period ending, days before the company sends the notice of redemption in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_NumberOfTradingDaysEndingBeforeNoticeOfRedemption
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period of time required to pass after the filing of a registration statement to become effective before warrant holders may be permitted to exercise warrants, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodForRegistrationStatementToBecomeEffective
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period of time required before warrants become exercisable after the completion of a Business Combination, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodRequiredForWarrantsToBecomeExercisable
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period for warrants to exercise after the completion of public offering, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodToExerciseWarrantsAfterPublicOfferings
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Period the entity is required to file a registration statement following the closing of a Business Combination, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_PeriodToFileRegistrationStatement
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

The product value issued upon exercise of warrants.

+ References

No definition available.

+ Details

Name:	fiac_ProductValueIssuedUponExerciseOfWarrants
Namespace Prefix:	fiac_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	duration

- Definition

Threshold period of specified trading days that common stock price exceeds threshold price per share, in PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

+ References

No definition available.

+ Details

Name:	fiac_TradingDaysThreshold
Namespace Prefix:	fiac_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	duration

- Definition

Exercise price per share or per unit of warrants or rights outstanding.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 505
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481112/505-10-50-3

+ Details

Name:	us-gaap_ClassOfWarrantOrRightExercisePriceOfWarrantsOrRights1
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

Number of securities into which each warrant or right may be converted. For example, but not limited to, each warrant may be converted into two shares.

+ References

No definition available.

+ Details

Name:	us-gaap_ClassOfWarrantOrRightNumberOfSecuritiesCalledByEachWarrantOrRight
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

Per share or per unit amount of equity securities issued.

+ References

No definition available.

+ Details

Name:	us-gaap_SharesIssuedPricePerShare
Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant

- References

No definition available.

+ Details

Name:	us-gaap_WarrantsAndRightsNoteDisclosureAbstract
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Period between issuance and expiration of outstanding warrant and right embodying unconditional obligation requiring redemption by transferring asset at specified or determinable date or upon event certain to occur, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents reported fact of one year, five months, and thirteen days.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 820
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (bbb)(2)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482106/820-10-50-2

+ Details

Name:	us-gaap_WarrantsAndRightsOutstandingTerm
Namespace Prefix:	us-gaap_
Data Type:	xbrli:durationItemType
Balance Type:	na
Period Type:	instant

- Details

Name:	us-gaap_ScheduleOfSharesSubjectToMandatoryRedemptionBySettlementTermsAxis=fiac_WarrantsAndRightsSubjectToMandatoryRedemptionOneMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	srt_RangeAxis=srt_MinimumMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ScheduleOfSharesSubjectToMandatoryRedemptionBySettlementTermsAxis=fiac_WarrantsAndRightsSubjectToMandatoryRedemptionTwoMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_ClassOfWarrantOrRightAxis=fiac_RedeemableWarrantsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_StatementClassOfStockAxis=us-gaap_CommonClassAMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Initial Public Offering, Public Warrants (Q3) (Details) - $ / shares		9 Months Ended	12 Months Ended
	Nov. 01, 2021	Sep. 30, 2023	Dec. 31, 2022	Sep. 30, 2022	Dec. 31, 2021
Public Warrants [Abstract]
Period to exercise warrants after public offerings		12 months	12 months
Period warrants to become excisable after business combination		30 days	30 days
Warrants expiration period		5 years	5 years
Period to file registration statement		20 days	20 days
Period for registration statement to become effective		60 days	60 days
Product value issued upon exercise of warrant (in dollars per share)	$ 0.361
Number of trading days		10 days	10 days
Redemption of Warrants When Price Equals or Exceeds $18.00 [Member]
Public Warrants [Abstract]
Warrant redemption price (in dollars per share)		$ 0.01	$ 0.01
Redemption of Warrants When Price Equals or Exceeds $18.00 [Member] \| Minimum [Member]
Public Warrants [Abstract]
Share price (in dollars per share)		$ 18	$ 18
Notice period to redeem warrants		30 days	30 days
Redemption of Warrants When Price Equals or Exceeds $10.00 [Member]
Public Warrants [Abstract]
Warrant redemption price (in dollars per share)		$ 0.1	$ 0.1
Redemption of Warrants When Price Equals or Exceeds $10.00 [Member] \| Minimum [Member]
Public Warrants [Abstract]
Share price (in dollars per share)		$ 10	$ 10
Notice period to redeem warrants		30 days	30 days
Public Warrants [Member]
Public Warrants [Abstract]
Number of trading days ending before notice of redemption		3 days
Class A Common Stock [Member]
Public Warrants [Abstract]
Number of shares issued upon exercise of warrant (in shares)		0	0	0	0
Share price (in dollars per share)		$ 11.5	$ 11.5
Class A Common Stock [Member] \| Redemption of Warrants When Price Equals or Exceeds $18.00 [Member]
Public Warrants [Abstract]
Number of trading days		20 days	20 days
Trading day threshold period		30 days	30 days
Class A Common Stock [Member] \| Redemption of Warrants When Price Equals or Exceeds $10.00 [Member]
Public Warrants [Abstract]
Number of trading days		20 days	20 days
Trading day threshold period		30 days	30 days
Class A Common Stock [Member] \| Public Warrants [Member]
Public Warrants [Abstract]
Number of shares issued upon exercise of warrant (in shares)	1
Exercise price of warrant (in dollars per share)	$ 11.5